The Taliban promised that the people of Afghanistan would not retaliate against the authorities or the regular military.
The Taliban has ordered its fighters to enter the Afghan capital, Kabul.
Afghan President Ashraf Ghani has reportedly fled the country.
A Taliban spokesman said officers and police had fled the city, raising security concerns.
The Afghan Interior Ministry said talks were underway to ensure a peaceful transfer of power.
In a reassuring message to Afghanistan, Taliban spokesman Suhail Shaheen told the BBC: “We promise that no one will retaliate against the people of Afghanistan.”
Russia plans to convene an emergency meeting of the Security Council to discuss the situation in Afghanistan.
Moscow has announced that it will not close its embassy in Kabul because it has received security guarantees from the Taliban.
A spokesman for the Russian embassy in Kabul said Moscow was ready to cooperate with the interim government in Afghanistan.
Twenty years after the Taliban entered Kabul, it was expelled after a US-led military invasion.
Image released, Getty Images
Afghans gathered in front of the passport office and visa centers for foreigners
Reports say many people in the Afghan capital are trying to reach Kabul airport, and some have left their cars on the road and walked to the airport due to traffic congestion.
There was chaos in Kabul, with many withdrawing at crowded ATMs, while others gathered in front of the passport office and visa centers abroad.
However, Shaheen told the BBC “people in Kabul should not worry, their lives and property are safe.”
He added: “We are in the service of this people and this country.”
He also stressed that the Taliban would give women the right to education and work.
U.S. President Joe Biden defended his decision to expedite the withdrawal of U.S. troops from Afghanistan, saying there was no justification for “an endless U.S. military presence in the country amid another civil conflict.”
The United States is evacuating its diplomatic missions and civilians from the US embassy in Kabul following reports that Americans are being flown in warplanes from Kabul airport.
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